Chapter 31: Q. 59 (page 903)

A cube of water 10 cm on a side is placed in a microwave beam having $E_{0} = 11 k V / m$ . The microwaves illuminate one face of the cube, and the water absorbs $80 %$ of the incident energy. How long will it take to raise the water temperature by $50 ˚ C ?$ .Assume that the water has no heat loss during this time.

Short Answer

Expert verified

The raise of the water temperature is $Δ t = 162 s$

Step by step solution

Definition of Electromagnetic fields and Waves:

A charge near its surroundings produces an electric field, which is a force. When other charges are brought near this field, they are subjected to this force. N/C (Force/Charge) is the SI unit for electric fields.

Given values:

$A = 0.10 m E_{0} = 11 k V / m T = 50 ˚$

Substitute the rate of energy values into equation:

$P = (80 %) I A$

$P = (0.80) \frac{c ε_{o}}{2} E_{o}^{2} A$

$P = (0.80) \frac{(3 \times 10^{8} m / s) (8.85 \times 10^{- 12} C^{2} / N \cdot m^{2})}{2} {(11 \times 10^{3} V / m)}^{2} (0.10 m)$

localid="1649933986875" $P = 1.29 k W$

Equation:

Now, Find value for $△ E$ :

$Δ E = m c Δ T$

$Δ E = (0.10 m)^{3} (1000 kg / m^{3}) (4186 J / kg / {}^{\circ}C) (50 ° C)$

$Δ E = 2.10 \times 10^{5} J$

Substitute the values in equation:

Finally, find the values for $△ t$ :

$Δ t = \frac{Δ E}{P}$

$Δ t = \frac{2.10 \times 10^{5} J}{1.29 \times 10^{- 3} W} △ t = 162 s$

Final Result:

The change in the quantity of water is $△ t = 162 s$ .

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Short Answer

Step by step solution

Definition of Electromagnetic fields and Waves:

Given values:

Substitute the rate of energy values into equation:

Equation:

Substitute the values in equation:

Final Result:

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A cube of water 10 cm on a side is placed in a microwave beam having E0=11kV/m. The microwaves illuminate one face of the cube, and the water absorbs 80%of the incident energy. How long will it take to raise the water temperature by 50˚C?.Assume that the water has no heat loss during this time.

Short Answer

Step by step solution

Definition of Electromagnetic fields and Waves:

Given values:

Substitute the rate of energy values into equation:

Equation:

Substitute the values in equation:

Final Result:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

Space Physics

Electrostatics

Fundamentals of Physics

Magnetism and Electromagnetic Induction

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.